E. Grandjean. The spectra of first-order sentences and computational complexity. SIAM Journal on Computing, 13:356--373, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... the class PSPACE and noninflationary fixpoint logic [Var82] cf. AV89] 1 The tight connection between descriptive and computational complexity, typically referred to as the connection between logic and complexity , was then proclaimed by Immerman [Imm87b] and studied by many researchers [Com88, Goe89, Gra84, Gra85, Gur83, Gur84, Gur88, HP84, Imm89, Lei89a, Liv82, Liv83, Lyn82, Saz80b, Saz80a, TU88]. 2 See [Imm89] for a survey. Although the relationship between descriptive and computational complexity is intimate, it is not without its problems, and the partners do have some irreconcilable differences. While computational devices work on encodings of problems, logic is applied directly to ....

E. Grandjean. The spectra of first-order sentences and computational complexity. SIAM Journal on Computing, 13:356--373, 1984.

.... i (c 1 (x 1 ) c n (x n ) where each c j is a possibly empty chain of compositions of the two functions succ( and pred( An example for such an occurrence is P (3) 1 (succ(succ(pred(x 1 ) succ(x 2 ) x 3 ) STRONG n ADIC NP is similar to the class GenSp(n8) defined by Grandjean [Gr84], the differences are: 1) his classes are like usually in finite model theory classes of graphs which use the signature [ 2) he allows existential quantification of functions, and (3) there is no restriction on the order of variables occurring in an n ary predicate. Lemma 8. 8n 1 : ....

E. Grandjean. The spectra of first-order sentences and computational complexity, SIAM Journal of Computing 13, 1984, pp. 356-373.

....subclasses of Binary NP that are still stronger than Monadic NP. One such subclass is obtained by restricting the SO quantification to unary functions. Grandjean has shown that this class contains all sets of strings that can be accepted in linear time by a nondeterministic successor RAM [Gra84, Gra85, Gra90] 1 . In [DLS95] other, semantical restrictions of the SO quantification were examined, e.g. linear orders, successor relations, equivalence relations, bijections. It turned out that all the resulting classes stay in a 3 level hierarchy with the respective representatives bijections, successor ....

E. Grandjean. The spectra of first-order sentences and computational complexity. SIAM Journal on Computing, 13:356--373, 1984.

....satisfying a first order formula. In order to make the above statements more precise we need some standard definitions from descriptive computational complexity that we introduce in a simplified manner which mixes together syntactical and semantical notions. For a rigorous treatment see [Fag74] Gra84] Imm89] Lyn82] Definition 2.1 A finite type is a finite sequence of nonnegative integers. Given a finite type T = n 1 ; n 2 ; n k ) a finite T structure is a (k 1) tuple F = X; f 1 ; f 2 ; f k ) where X is a non empty finite set called the domain of the structure F ....

E. Grandjean. The spectra of first-order sentences and computational complexity. SIAM Journal on Computing, 13(2):356--373, 1984.

.... class PSPACE and noninflationary fixpoint logic [Var82] see also [Imm82] 1 The tight connection between descriptive and computational complexity, typically referred to as the connection between logic and complexity , was then proclaimed by Immerman [Imm87b] and studied by many researchers [Com88, Goe89, Gra84, Gra85, Gur83, Gur84, Gur88, HP84, Imm89, Lei89a, Liv82, Liv83, Lyn82, Saz80b, Saz80a, TU88]. 2 See [Imm89] for a survey. Although the relationship between descriptive and computational complexity is intimate, it is not without its problems, and the partners do have some irreconcilable differences. While computational devices work on encodings of problems, logic is applied directly ....

E. Grandjean. The spectra of first-order sentences and computational complexity. SIAM Journal on Computing, 13:356--373, 1984.

....satisfying a first order formula. In order to make the above statements more precise we need some standard definitions from descriptive computational complexity that we introduce in a simplified manner which mixes together syntactical and semantical notions. For a rigorous treatment see [Fag74] Gra84] Imm89] Lyn82] Definition 2.1 A finite type is a finite sequence of non negative integers. Given a finite type T = n 1 ; n 2 ; n k ) a finite T structure is a (k 1) tuple F = X; f 1 ; f 2 ; f k ) where X is a non empty finite set called the domain of the structure F ....

E. Grandjean. The spectra of first-order sentences and computational complexity. SIAM Journal on Computing, 13(2):356--373, 1984.

.... the class PSPACE and noninflationary fixpoint logic [Var82] cf. AV89] 1 The tight connection between descriptive and computational complexity, typically referred to as the connection between logic and complexity , was then proclaimed by Immerman [Imm87b] and studied by many researchers [Com88, Goe89, Gra84, Gra85, Gur83, Gur84, Gur88, HP84, Imm89, Lei89a, Liv82, Liv83, Lyn82, Saz80b, Saz80a, TU88]. 2 See [Imm89] for a survey. Although the relationship between descriptive and computational complexity is intimate, it is not without its problems, and the partners do have some irreconcilable differences. While computational devices work on encodings of problems, logic is applied directly to ....

E. Grandjean. The spectra of first-order sentences and computational complexity. SIAM Journal on Computing, 13:356--373, 1984.

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E. Grandjean. The spectra of first-order sentences and computational complexity. SIAM Journal on Computing, 13:356--373, 1984.

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Etienne Grandjean, "The Spectra of First-Order Sentences and Computational Complexity," SIAM J. of Comp. 13, No. 2, 1984, (356-373).

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Etienne Grandjean, The Spectra of First-Order Sentences and Computational Complexity, SIAM J. of Comp. 13, No. 2 (1984), 356-373.

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